The invention relates to the suspension of an elevator car of an elevator and to producing lifting force for the elevator car. The ropes of the suspension roping of elevators have conventionally been manufactured from metal. Known in the art are also elevators in which is used hoisting roping comprising ropes having a force-transmission capability based on light fibers, such as glass fibers or carbon fibers, in essentially the longitudinal directions of the rope. This type of solution is presented in, inter alia, publication WO 2009090299. In the solution the rope has (a) load-bearing composite part(s), which composite part comprises reinforcing fibers in a polymer matrix. Another problem of composite solutions has been that composite parts do not bend well around a small diverting pulley. That being the case also the suspending rope pulleys and the traction sheave have been large in diameter. Owing to a large traction sheave, the dimensioning of the motor of the machine to be of a small size has been hampered by the large torque required of the motor. Owing to costs and size increase, a gear has not been desired for the machine either. That being the case, the aforementioned structure of the suspension ropes has resulted in a machine that is large in size. Additionally, the aforementioned types of ropes withstand the forces exerted on the surface of the rope worse than conventional metal ropes. Metal ropes withstand e.g. impacts, incisions and abrasion well. To eliminate these problems, ropes of a more brittle material are coated with polyurethane or with some other elastic coating. Yet another problem in coated composite ropes is the long-term permanence of attachment of the coating to a rigid load-bearing part, more particularly in solutions in which lifting force is transmitted via the coating or frequently repeated braking is transmitted to the roping via a rotating traction means, because in these functions sudden shearing forces are produced between the thin coating and the generally smooth composite. This can result in local detachment of the coating and the composite from each other. Likewise, configuring the friction coefficient to be suitably large within certain limits has been challenging.